By the quasi-periodicity we further have that the elementwise product of a DZT \(Z_x\)  with the complex conjugate DZT \(Z_y^{\ast }\)  is periodic in \(n\)  and \(k\) . Motivated by the periodicity, we can apply a two-dimensional DFT, which turns out to be [1]}, [2]}
\(\sum _{n=0}^{L-1}\sum _{k=0}^{K-1} [n,k] Z_{y}^\ast [n,k] e^{j2\pi \left(\frac{m}{K}k-\frac{l}{L}n\right)} = \langle x, y_{m,l} \rangle ,\) 
